The incomplete LU-decomposition as a relaxation method in multi-grid algorithms
Piet Hemker · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1980
We consider relaxation methods for use with Multi-Grid (MG-) algorithms to solve a sparse linear system l > 0, which is supposed to be the discretization of a continuous boundary value problem Ax = f.With the same equation coarser discretizations are related:we first give a brief exposition of the framework of MG-methods.Next, we describe the incomplete LU-decomposition as a relaxation method and in the 3rd section we compare different variants of it.The conclusion is in favour of the ILU variant. THE MULTI-GRID FRAMEWORKConsidering MG methods in which each iteration step consists of Y coarse grid correction steps, preceeded by p and followed by q relaxation sweeps, we see that in each MG iteration step the residual is multiplied by the operator (cf.[2]) -MLA -TLA -REL q k -1 (MTLA) y k-1 (REL)p Mk Mk + (~ ) Ak pk-1 ~-1 k-1